Solve the Problem $f ( t ) = 3 t$ On the Interval

Multiple Choice

Solve the problem.
-Find the nth-order Fourier approximation to the function $f ( t ) = 3 t$ on the interval $[ 0,2 \pi ]$ .

A) $\pi - \cos ( t ) - \cos ( 2 t ) - \cos ( 3 t ) - \ldots - \frac { 6 } { n } \cos ( n t )$
B) $3 \pi - 6 \cos ( t ) - 3 \sin ( 2 t ) - 2 \cos ( 3 t ) - \ldots - \frac { 6 } { n } \cos ( n t )$
C) $3 \pi - 6 \sin ( t ) - 3 \sin ( 2 t ) - 2 \sin ( 3 t ) - \ldots - \frac { 6 } { n } \sin ( n t )$
D) $3 \pi - 6 \sin ( t ) - 3 \sin ( 2 t ) - 1 \sin ( 3 t ) - \ldots - \frac { 3 } { n } \sin ( n t )$